Something to try, though I can't guarantee it will fix it:
1) Download the
non-beta 2.1 drivers released November 1st.
2) Run the DisplayLink Software Uninstaller.app to completely remove the current (and any previous) DisplayLink Drivers. (Then Reboot)
3) Run DisplayLink Software Installer.pkg to re-install the latest drivers.
4) Open Finder, go to Applications -> Utilities and run Disk Utility.app, select your Mavericks partition (Typically Macintosh HD unless you've renamed it) then click the Repair Disk Permissions button. When completed, reboot one more time.
With any luck, hopefully this will resolve your issue.